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Reliable solutions of problems in the deformation theory of plasticity with respect to uncertain material function

Ivan Hlaváček (1996)

Applications of Mathematics

Maximization problems are formulated for a class of quasistatic problems in the deformation theory of plasticity with respect to an uncertainty in the material function. Approximate problems are introduced on the basis of cubic Hermite splines and finite elements. The solvability of both continuous and approximate problems is proved and some convergence analysis presented.

Remarks on Carleman estimates and exact controllability of the Lamé system

Oleg Yu. Imanuvilov, Masahiro Yamamoto (2002)

Journées équations aux dérivées partielles

In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.

Remarques sur les équations linéaires elliptiques du second ordre sous forme divergence dans les domaines non bornés

Pierre Louis Lions (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra resistenza e l'unicità della soluzione del problema A u = f , u H 0 1 ( Ω ) nel caso in cui Ω è un aperto di n non limitato, A è un operatore variazionale ellittico del secondo ordine a coefficienti misurabili e limitati e f appartiene a H - 1 ( Ω ) .

Renormalized solution for nonlinear degenerate problems in the whole space

Mohamed Maliki, Adama Ouedraogo (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the general degenerate parabolic equation : u t - Δ b ( u ) + d i v F ˜ ( u ) = f in Q = ] 0 , T [ × N , T > 0 . We suppose that the flux F ˜ is continuous, b is nondecreasing continuous and both functions are not necessarily Lipschitz. We prove the existence of the renormalized solution of the associated Cauchy problem for L 1 initial data and source term. We establish the uniqueness of this type of solution under a structure condition F ˜ ( r ) = F ( b ( r ) ) and an assumption on the modulus of continuity of b . The novelty of this work is that Ω = N , u 0 , f L 1 , b , F ˜ are not Lipschitz...

Resonant delocalization for random Schrödinger operators on tree graphs

Michael Aizenman, Simone Warzel (2013)

Journal of the European Mathematical Society

We analyse the spectral phase diagram of Schrödinger operators T + λ V on regular tree graphs, with T the graph adjacency operator and V a random potential given by i i d random variables. The main result is a criterion for the emergence of absolutely continuous ( a c ) spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials a c spectrum appears at arbitrarily weak disorder ( λ 1 ) in an energy regime which extends beyond the spectrum of T . Incorporating...

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